Instead of proving a matrix wasn't reachable with only row operations the smart way, I just made this script to generate ALL reachable matrices.
Run python matrix_graph_gen.py --help
for usage info.
Matrices can be provided in any of the following forms:
- Pythonic
[[1,2,3],[4,5,6],[7,8,9]]
- Lazy Pythonic
[1,2,0][2,0,1][1,1,1]
- Latex
1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1
Just remember: you're entering these on the command line, so you probably need to wrap these in "quotes" to have them load properly.
From experience, the graphs this script generates are far too large for Plantuml or Graphviz to handle directly.
I have found the most success using Gephi to analyze the dot file output.